Is this graph transformation G_1 to G_2 efficiently computable?

- All vertices in G_1 are unique edges in G_2
- Adjacent vertices in G_1 are adjacent edges in G_2

The inverse transformation (edges to vertices) is trivial.

I can encode it as CSP, but I am not sure solving is tractable:

adjacent V1,V2 in G_1 to (V1',V1''), (V2',V2'') in G_2, must share a vertex, constraints: V1'=V2' / V1'=V2'' / V1''=V2' / V1''=V2'' and some disequations.

References, search terms will be apreciated. Thank you.